Solve 50a+120*3000-60a/40leq7800

$$50 a + 120 \cdot \frac { 3000 - 60 a } { 40 } \leq 7800$$

Solve for a

$$a\geq \frac{120}{13}$$

Solution Steps

Multiply both sides of the equation by 40. Since 40 is positive, the inequality direction remains the same.

$$2000a+120\left(3000-60a\right)\leq 312000$$

Use the distributive property to multiply 120 by 3000-60a.

$$2000a+360000-7200a\leq 312000$$

Combine 2000a and -7200a to get -5200a.

$$-5200a+360000\leq 312000$$

Subtract 360000 from both sides.

$$-5200a\leq 312000-360000$$

Subtract 360000 from 312000 to get -48000.

$$-5200a\leq -48000$$

Divide both sides by -5200. Since -5200 is negative, the inequality direction is changed.

$$a\geq \frac{-48000}{-5200}$$

Reduce the fraction \frac{-48000}{-5200} to lowest terms by extracting and canceling out -400.

$$a\geq \frac{120}{13}$$